It is known that a polysaccharide having an anti-tumour effect can be produced by refining the extract of the Basidiomycetes with an aqueous solvent. This known method, however, has a serious defect that extraction efficiency of the active components is low and hence practical adaptability of this method to industrial production of the anti-tumour substances is poor. This method employes salting-out by use of ammonium sulfate, dialysis, precipitation by use of an organic solvent, or gel filtration as the extract refining means, but such refining means are extremely poor in workability, and hence such method is not of a type advantageous for removing the low molecular weight substances (with molecular weight of less than 5,000) contained in the extract. The low molecular weight substances have almost nil inhibitory activity against Sarcoma-180 solid tumours in mice in intra-peritoneal administration, and further, they have bitterness and a disagreeable odor, so that presence of such substances is undesirable in utilization of the polysaccharides as medicaments.